We employ cosmological hydrodynamical simulations to study the growth of massive black holes (BHs) at high redshifts subject to BH merger recoils from gravitational wave emission. We select the most massive dark matter halo at z=6 from the Millennium simulation, and resimulate its formation at much higher resolution including gas physics and a model for BH seeding, growth and feedback. Assuming that the initial BH seeds are relatively massive, of the order of 10^5 Msun, and that seeding occurs around z~15 in dark matter haloes of mass 10^9-10^10 Msun, we find that it is possible to build up supermassive BHs (SMBHs) by z=6 that assemble most of their mass during extended Eddington-limited accretion periods. The properties of the simulated SMBHs are consistent with observations of z=6 quasars in terms of the estimated BH masses and bolometric luminosities, the amount of star formation occurring within the host halo, and the presence of highly enriched gas in the innermost regions of the host galaxy. After a peak in the BH accretion rate at z=6, the most massive BH has become sufficiently massive for the growth to enter into a much slower phase of feedback-regulated accretion. We explore the full range of expected recoils and radiative efficiencies, and also consider models with spinning BHs. In the most `pessimistic case where BH spins are initially high, we find that the growth of the SMBHs can be potentially hampered if they grow mostly in isolation and experience only a small number of mergers. Whereas BH kicks can expel a substantial fraction of low mass BHs, they do not significantly affect the build up of the SMBHs. On the contrary, a large number of BH mergers has beneficial consequences for the growth of the SMBHs by considerably reducing their spin. [Abridged]
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